458 石 油 学 会 誌 Sekiyu Gakkaishi, 36, (6), 458-466 (1993)
[Regular Paper] Minimum Reflux Calculations for Heterogeneous Azeotropic Distillation Processes
Fang-Zhi LIU, Hideki MORI*, Setsuro HIRAOKA, and Ikuho YAMADA
Dept. of Applied Chemistry, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466
(Received December 16, 1992)
An algorithm is presented for solving operating type minimum reflux problems of heterogeneous azeotropic distillation processes, based on the concept of hypothetical pinch plate proposed by Yamada et al. The process discussed here is restricted to column sequence in which the entrainer recycle stream returns to the azeotropic column as a feed stream and which is favourable over the other sequences in respect to energy consumption. A design technique is also proposed to simultaneously calculate the inner and outer minimum reflux ratios of azeotropic column, the minimum reflux ratio of recovery column, and the optimal recycle flow rate. The algorithm and the design technique are illustrated by numerical examples of ethanol dehydration with benzene.
1. Introduction the pinch point in the stripping section; (2) one pure component is obtained in bottoms stream; The calculation of minimum ref lux ratios is an and (3) the mole fraction ratio of light and heavy important and extremely difficult problem in key components at the pinch point in the stripping calculations and design of distillations. Any section is equal to that in feed composition. Since excess ref lux will not only lead to an increased this method is simple and easy to use, and no other energy consumption but also larger column method is available, the graphical analysis method diameters and heat exchanger areas. The mini- has been used to estimate the minimum reflux in mum ref lux provides us a valuable piece of the design of azeotropic columns, though its information on the actual energy consumption of accuracy is sometimes not satisfactory. The columns. Columns can also be designed quickly boundary-value procedure5) is also based on the and with confidence when minimum reflux rates constant molar overflow assumption. This are known for given specifications. assumption is obviously incorrect for heteroge- Some important methods or procedures have neous azeotropic distillation systems. Further- been published in the area of minimum reflux more, the boundary-value procedure is based on calculations. They can be classified into two dew point calculations in rectifying section, but groups: shortcut methods and rigorous methods. dew point calculations often fail on top stages of a The well-known shortcut methods are the heterogeneous azeotropic column, when the vapor Underwood method or its relatives1)-3). Neverthe- compositions are close to the heterogeneous less, since these methods are based on the as- azeotrope. sumptions of constant relative volatility and The rigorous methods are based on the constant molar overflow, they are not suitable to characteristic of pinch points and the physical distillations of strongly nonideal mixtures. For connection between pinch points and column end determining the minimum reflux of heteroge- compositions. Typical methods of rigorous neous azeotropic columns, Yorizane et al.4) methods are those reported by McDonough and proposed a graphical analysis method and Pham et Holland6), Chien7), and Yamada and coworker8)-10). al.5) proposed a boundary-value procedure. The Except for Yamada's method, however, these graphical analysis method4) is limited to ternary methods were only tested on ideal mixtures. To systems and based on the assumptions of (1) our knowledge, no rigorous method has been constant molar overflow between the top stage and reported to calculate the minimum ref lux of heterogeneous azeotropic columns or processes, * To whom correspondence should be addressed. and because the assumption of constant molar
石 油 学 会 誌 Sekiyu Gakkaishi, Vol. 36, No. 6, 1993 459 overflow largely deviates from practice, a rigorous rate as stated by Doherty et al.11),12), they have method of minimum reflux calculation is neces- almost been replaced by the configuration shown sary for heterogeneous azeotropic distillation in Fig, 1c in practice. Our discussion here, columns. therefore, is restricted to the process shown in Fig. The literature contains many options of con- 1c. figurations for heterogeneous azeotropic distilla- In this work, we proposed a procedure for tion processes. These configurations generally solving the minimum reflux problem of hetero- consist of either two or three columns with various geneous azeotropic distillation systems based on options for handling the entrainer recycle stream. the hypothetical pinch plate model proposed by Several typical configurations are given in Figs. Yamada8). Furthermore, a design technique is 1a-1c. The earlierindustrial processes used to developed to determine simultaneously the inner employ the configurationsshown in Figs. 1a and and outer minimum reflux ratios of azeotropic 1b, i.e.the entrainerrecovery column only consists columns, the minimum reflux ratio of entrainer stripping section and the entrainer recycle stream recovery columns, and the optimal flow rate of the is returned directly to the decanter. Since these recycle stream based on the energy consumption kinds of configurations require a large recycle flow consideration for a given separation requirement.
2. Modeling
2.1. Inner Reflux and Outer Reflux To design the distillation process shown in Fig. 1c, determination of three reflux ratios: inner reflux ratio Ri, outer reflux ratio Ro, and reflux ratio of recovery column R', as defined below are required.
(1)
Fig. 1a A Two-column Process with a Recycle Stream to the Decanter (2)
(3)
The relationship between Ri, Ro, and an overall reflux ratio of the azeotropic column R is as follows.
(4)
The feed rate of the recovery column, D, is Fig. 1b A Three-column Process usually much smaller than the flow rates of aqueous phase in the decanter if all the overhead vapor V1 is condensed and subcooled, and then put into the decanter. Furthermore, the decanter temperature is much lower than the saturated temperature of the reflux liquid. Therefore, the introduction of inner reflux LiR can not only reduce energy consumption but also improve the sepa- ration of the azeotropic column. 2.2. Pinch Points and Decomposition Strategy When a column is operated at minimum reflux, the number of stages in the rectifying and stripping sections should be infinite to satisfy separation
Fig. 1c A Two-column Process with a Recycle Stream requirements. Under this condition, there will be to the Azeotropic Column two pinch points, one is between the feed stage and
石 油 学 会 誌 Sekiyu Gakkaishi, Vol. 36, No. 6, 1993 460 the top stage and one between the feed stage and the 2.3. Decanter (#1) reboiler, no matter whether or not all components The isothermal liquid-liquid equilibrium in are distributed to the top and bottom products. the decanter can be described by the following This is also true for the columns of the azeotropic equations, supposing complete separation of two distillation process under consideration. liquid phases in it. Since a recycle stream is included in the azeotropic distillation process, the whole process L0=LI+LII (5) shown in Fig. 1c has to be modeled in order to solve rigorously the minimum reflux problem of the L0y1i=LIxIi+LIIχIIi (6) process. To model the process, it is decomposed into two xIi=KLixIIi (7) columns by breaking up the recycle stream and each column is further decomposed into several (8) sections as shown in Figs. 2a and 2b. In the following discussion, the theoretical stage and the 2.4. Top Section of Azeotropic Column (#2) adiabatic column assumptions are used. At the hypothetical pinch plate, the downcom- ing liquid and the upflowing vapor streams are in equilibrium. For the upper hypothetical pinch plate (HI) of the azeotropic column, the following equation is obtained.
yHI,i=KHI,iχHI,i (9)
(10)
Besides, the top section of the azeotropic column as shown in Fig. 2a can be described by the following balance equations.
VHI+LoR=LHI+L0 (11)
VHIyHI,i+LoRχoRi=LHIxHI,i+L0y1i (12)
VHIHHI+LoRhoR=LHIhHI+L0h0+Ｑc (13)
Fig. 2a An Azeotropic Column at Minimum Reflux 2.5. Bottom Section of Azeotropic Column (#3) Similar to the top section, the section below the lower hypothetical pinch plate (HII) can be described by the following equations.
(14)
(15)
(16)
(17)
(18)
2.6. Middle Section of Azeotropic Column (#4) As is proposed by Yamada et al.9), the number of stages between the two hypothetical pinch plates is assigned to an arbitrary finite number which can satisfy Eqs. (9) and (14). For this section, input Fig. 2b A Recovery Column at Minimum Reflux streams are Ft, VHIIand LHI and output streams are
石 油 学 会 誌 Sekiyu Gakkaishi, Vol. 36, No. 6, 1993 461
VHI and LHII. It can be dealt with as a column Since the reflux to the azeotropic column without condenser and reboiler. Any one stage of consists of inner reflux and outer reflux, one this section can be described by the MESH more degree of freedom remains. Here, β is (Material balance, Equilibrium, Summation of specified and it is defined as follows. mole fraction, and Heat balance) equations. 2.7. Entrainer Recovery Column φ=LI/LII (29) The recovery column is decomposed into three sections as shown in Fig. 2b. Similar to the Romin=βφ azeotropic column, the middle section between the β≧1} (30) two hypothetical pinch plates is also dealt with as a column with a finite number of stages. The top Where φ is the relative proportion of the flow rates and bottom sections are described by the following of two liquid phases in the decanter. equations. Since β≧1, the distillate D consists of only the
For the top section (#5): phase II. Thus,
y'HI,i=K'HI,ix'HI,i (19) xDi=xIIi (31)
L0=(1+βφ)D=(1+βφ)(B'+D') (32) (20)
V'HI=L'HI+D' (21) (33)
V'HIy'HI,i=L'HIx',HI,i+D'x'Di (22) 3.2. Algorithm
After the process is specified as stated above, the V'HIH'HI=L'HIh'HI+D'h'D+Q'c (23) bottoms compositions of two columns and the vapor and liquid stream compositions at hy-
For the bottom section (#6): pothetical pinch plates can be calculated by the following algorithm.
y'HII,i=K'HII,ix'HII,i (24) 1) Give initial estimates of y1i, and solve Eqs.
(5)-(8) and Eqs. (29)-(33) for xIi, xIIi,φ, Romin, xDi, C∑i=1y'HII,i-1=0 (25) xoRi and LoR. 2) Give initial estimates of x'HIi and x'HII,i. L'HII=V'HII+B' (26) 3) Solve Eqs. (19)-(23) for y'HI,i, x'Di, L'HI, and V'HI. (27) 4) Solve Eqs. (24)-(28) for y'HII,i, x'Bi, L'HII, and V'HII. L'HIIh'HII+Q'r=V'HIIH'HII+B'h'B (28) 5) Solve the middle section between the two hypothetical pinch plates of the recovery column
3. Algorithm for Minimum Reflux Problem of to update y'HI,i, V'HI, x'HII,i, and L'HII. In this work, Operating Type this section is stagewisely solved by the flash calculation procedure used in our previous 3.1. Specifications articles13), 14). The convergence tolerance is taken
For an operating type problem of the azeotropic as follows distillation process shown in Fig. 1c, the following variables should be specified. ● Feed conditions, such as F, xFi, and TF (34) ● Entrainer makeup rate Ei ● Decanter temperature Td, operating Pressures 6) Correct x'HI,iand x'HII,iusing Eqs. (35) and (36). of azeotropic and recovery columns ● Recycle flow rate D' ● Bottoms rate B or B' (35) ● The number of stages Of rectifying section and
stripping section of each column. For the minimum reflux ratio problem, all these (36)
numbers of stages are specified as infinite. ● The minimum reflux ratios Rmin and R'min.
石 油 学 会 誌 Sekiyu Gakkaishi, Vol. 36, No. 6, 1993 462
stop; otherwise, return to step 1) and then use the updated y1i and repeat the calculations. Where θHI=[C∑i=1V'HI,ix'HI,i/D'x'Di+L'HIx'HI,i(x'HI,i)as]-1 (37)
∑i|yk+11i-yk1i|≦ε4 (46)
θHII=[c∑i=1DXDi/D'x'Di+B'x'Bi(x'HII,i)as]-1 (38) 3.3. Numerical Example The azeotropic distillation process of ethanol 7) Repeat the calculations of steps 3) to 6) till the dehydration with benzene is taken as an example following tolerance is satisfied. and the feed conditions and some specifications are given in Fig. 3. The overall minimum ref lux ratio of the ∑i|1-D'x'Di+B'x'Bi/DxDi|≦ ε1 (39) azeotropic column and the minimum reflux ratio of the recovery column are specified as Rmin=8.0 8) Calculate the feed rate and compositions of and R'min=0.45, respectively. The most effective the azeotropic column by Eqs. (40) and (41). Take separation in the decanter is achieved when the the outer reflux (LoR and xoRi)as a feed to the top β=1 in Eq. (30) and this can easily be reached by stage of the azeotropic column. controlling the flow rate L0 according to the two liquid levels in the decanter. Therefore, the factor
Ft=F+D' (40) β is specified as β=1 in this example. The columns are operated at atmospheric (41) pressure. Entrainer make-up rate E is specified as zero. Vapor-liquid equilibria is calculated using 9) Give initial estimates of xHI,i and xHII,i. the NRTL parameters of Gmehling and 10) Solve Eqs. (9)-(13) for yHI,i, y1i, LHI, and VHI. Onken13),15). Liquid-liquid equilibria in the 11) Solve Eqs. (14)-(18) for yHII,i, xBi, LHII, and decanter is predicted by the NRTL parameters of VHII. Sorensen and Arlt16). The enthalpy is calculated 12) Solve the middle section of the azeotropic by the method proposed by Prausnitz et al.17). column to update yHI,i and XHII,i. This section is The middle section stage numbers N and M have also stagewisely solved by the flash calculation been specified as 30 and the feed stages are specified procedure used in our previous articles13),14). The as 20 counted from the top. These stage numbers convergence tolerance is taken as follows are large enough to satisfy the following tol- erances.
(42) ∑|y2i-KHI,ixHI,i｜<10-6 (47) Before the tolerance given in Eq. (45) is reached, ∑|yHII,i-KN-1,ixN-1,i|<10-6 } the calculated yHI,iand XHII,imay not satisfy the Eqs. ∑|y'2i-k'HI,ix'HI,i|<10-6 (9) and (14). } (48) 13) Correct XHI,iand XHII,iby Eqs. (43) and (44) ∑|y'HII,i-K'M-1,ix'M-1,i|<10-6
(43)
(44)
Similar to those stated in step 6),θI and θII are factors to make the summation of corrected xHI,i and xHII,i equal to unity.
14) Repeat the calculations of steps 10) to 13) till
the following tolerance is satisfied.
(45) Fig. 3 A Flow Sheet of Ethanol (1)/Benzene (2)/Water (3) Azeotropic Distillation Process at Minimum 15) If Eq. (46) is satisfied, then output results, and Reflux Ratios
石 油 学 会 誌 Sekiyu Gakkaishi, Vol. 36, No. 6, 1993 463
The calculated results of this example are given As shown in Table 1 and Figs. 4 and 5, this in Table 1. The calculated composition profiles algorithm can provided not only the bottoms com- between the two hypothetical pinch plates are positions but also pinch point locations and the shown in Figs. 4 and 5 for the two columns, flow rates and compositions of vapor and liquid respectively. phases at the pinch points. At the same times, the two liquid phase compositions in decanter and suitable inner and outer reflux ratios, Rimin and Romin, Table 1 Calculated Results are determined from the overall minimum reflux ratio Rmin and the specified β. Since the assumptions of constant relative volatility and constant molar overflow are not used in the proposed algorithm, the accuracy of calculated results is high.
4. Algorithm for Minimum Reflux Problem of Design Type
Design type problem is often more important than that of operating type in practice. Because of high nonideality of heterogeneous azeotropic systems, however, the minimum reflux ratios cannot be accurately calculated by available methods. In the following, the authors discuss a procedure to determine Rimin, Romin, R'min, and optimal recycle flow rate Dopt based on the operating type algorithm discussed above. 4. 1. Specifications Instead of specifying Rmin and Rmin, the sepa- ration requirements such as product purities of the key components of each column are specified for the design type problem. In order to achieve the same separation, D' and R'minhave to compensate each other; if D' is small, R'minhas to be large in order to remove the water in the original feed, and vise versa. Furthermore, there is similar relationship between Rmin and
Fig. 4 Calculated Results for Middle Section of D(=D'+B'). From the view of energy consump- Azeotropic Column tion and equipment size, smaller D', Rmin, and R'min are favored. Thus, there exists a optimal recycle rate D'opt. Here, we employ Eq. (49) instead of specifying D' as the case of operating type problem since the equipment cost and the operating cost are directly related to the vapor flow rates of the columns.
(Rmin+1)D+ρ(R'aim+1)D'→minimum (49)
where ρ is a factor considering the difference of the equipment and operating cost per unit vapor rate between the azeotropic column and the recovery column. The other specifications are the same as those for the operating type problem. Fig. 5 Calculated Results for Middle Section of Recovery 4.2. Algorithm Column The golden section method is used to search for
石 油 学 会 誌 Sekiyu Gakkaishi, Vol. 36, No. 6, 1993 464
the D'opt basedon the objective function of Eq. (49) Table 2 Results of Design Type Example in the outer loop. For a given D', execute the steps 1) to 5) stated below, to calculate Rimin, Romin, and
R' min 1) Give initialestimate of y1i. The results of simulation of azeotropic columns at finite reflux have shown that y1i is very close to the distillation boundary between the ethanol/ benzene azeotrope and the ternary azeotrope13) Furthermore, y1iis also subject to the following two restrictions. 1. Phase-splitting must occur in the decanter. 2. Phase-splitting should not occur on top stages of the azeotropic column. Consequently, the initial estimates of y1i can be given easily and accurately. 2) Solve Eqs. (5)-(9) and Eqs. (31)-(34) for xIi, xIIi,φ, D, and xDi. 3) Take the Eq. (50) as the objective function to search for R'min using the golden section method.
|(x'B,water)cal-(x'B,water)spe|→0 (50)
For a given R'min,calculate x'Biusing the same steps as the steps 2)-7) stated in 3.2. Fig. 6 Recycle Flow Rate and Total Overhead Vapor 4) Take the Eq. (51) as the objective function to Flow Rate of Azeotropic and Recovery Columns search for Rimin using the golden section method.
|(xB,ethanol)cal-(xB,ethanol)spe|→0 (51)
For a given Rimin, calculate xBi using the same steps as the steps 8)-14) stated in 3.2. 5) Check y1i by Eq. (45). If it is not satisfied, update y1i,return to step 2). 4.3. Example and Results The distillation process shown in Fig. 3 is also taken as an example. However, the problem here is to calculate the Rimin,Romin, Romin,R'min, R'min,and D'opt and totoD'opt satisfysatisfy the separation requirement xB,ethanol≧99.99% and x'B,water≧99.99%. For this example, the β and ρ have been taken as unity.
The results calculated with the proposed Fig. 7 Specifications of an Azeotropic Column procedure are given in Table 2. Although there are three optimization loops using the golden section method in the proposed algorithm, the azeotropic column shown in Fig. 7 is simulated by computation time is not very long, because only the steady-state simulation algorithm proposed in less than ten iterations are needed for one use of the our previous article13). The feed conditions of golden section method. Furthermore, since the this column are same with those given in Fig. 3. initial estimate y1i can be accurately given, Eq. (46) The recycle stream and the outer reflux are taken as is easily satisfied. the feeds of the column and their flow rates (D', LoR) The relationship between D' and the objective and compositions (x'Di, xoRi) are taken from the function defined by Eq. (49) is shown in Fig. 6. calculated results given in Table 2. By taking the This figure shows that the total vapor flow rate of operating reflux ratio as Razeo=λRimin, the azeotropic two columns is sensitive to the recycle flow rate D'. column is simulated and the calculated results for To examine the calculated minimum reflux three reflux ratios are given in Table 3. These ratios obtained by the above procedure, an results show that the operating reflux ratio of an
石 油 学 会 誌 Sekiyu Gakkaishi, Vol. 36, No. 6, 1993 465
Table 3 Simulation Results of a Designed Azeotropic y: vapor mole fraction [-] Column β: factor for reflux distribution [-] ε: convergence tolerance [-] θ: factor to generalize mole fractions [-] λ: constant for determining reflux ratio from minimum reflex ratio [-]
ρ: afactor consideringdifference costher unitvalor rate between azeotropic and recovery columns [-]
φ: molar ratio of two phases in decanter [-]
石 油 学 会 誌 Sekiyu Gakkaishi, Vol. 36, No. 6, 1993 466
Jpn., 24, 132 (1991). Data Collection", DECHEMA Chem. Ser. Vol. V, Part 2, 15) Gmehling, J., Onken, U., "Vapor-Liquid Equilibrium (1980), p. 354-605. Data Collection", DECHEMA Chem. Ser. Vol. I, Part 1, 17) Prausnitz, J. M. et al., "Computer Calculations for (1977), p. 642. Multicomponent Vapor-liquid and Liquid-liquid 16) Sorensen, J. M., Arlt, W., "Liquid-Liquid Equilibrium Equilibria", Prentice-Hall, (1980).
要 旨
不均一 系共沸 蒸留の最小還流計算
劉 芳 芝, 森 秀樹, 平岡節郎, 山田幾穂 名古屋工業大学応用化学科, 466名 古屋市昭和区御器所町
不 均 一 共 沸 蒸 留 プ ロセ ス に対 して, 山 田 らが 提 出 した仮 想 ピ 解 法 で は, 操 作 型 解 法 に黄 金 分 割 法 を組 み 込 み, 分 離 要 求 を満 ンチ 段 の 概 念 に基 づ く, 操 作 型 お よ び設 計 型 最 小 還 流 問 題 の解 足 した 上 で, 共 沸 塔 と回 収 塔 の 塔 内 蒸 気 流 量 を最 小 とす る最 適 法 を提 出 す る。 い ろい ろ な プ ロセ ス構 成 の な かで,本 研 究 は エ リサ イ クル 流 量, 共 沸 塔 の 最 小 内 還 流 比 と最 小 外 還 流 比, お よ ネ ル ギー 的 に一 番 有 利 と考 え られ, 現 在 多 く採 用 さ れ て い る プ び 共 沸 剤 回 収 塔 の 最 小 還 流 比 を同 時 に決 定 す る。 ベ ンゼ ンに よ ロセ ス を対 象 とす る。 操作 型 解 法 で は, 共 沸 塔 の塔 頂 蒸 気 組 成 る エ タ ノー ル 脱 水 共 沸 蒸 留 プ ロセ ス を計 算 例 と して こ れ らの 方 の仮 定 値 にお ける デ カ ン ター の 液 相 分 離 計 算 か ら始 め, 仮 想 ピ 法 の 有 用性 を検 討 した。 この 設 計 型 の 最 小 還 流 計 算 法 に よ り得 ンチ 段 に よ って 分 割 され る 各 セ ク シ ョン を順 次 解 き, 逐 次 代 入 られ た 解 の 妥 当 性 を有 限 還 流 シ ミュ レー シ ョ ン法 で 検 証 す る。 法 に よ って 共 沸 塔 の 塔 頂 蒸 気 組 成 を収 束 させ る。 また, 設 計 型
Keywords Distillation, Heterogeneous azeotropic distillation, Minimum reflux ratio
石 油 学 会 誌 Sekiyu Gakkaishi, Vol. 36, No. 6, 1993